Why Are There Different Results in Young's Double-Slit Experiment Calculations?

[Chris Okeef]

Homework Statement

In a KhanAcademy video, light of wavelength 700nm shines through a double-slit whose holes are spaced 1300nm
apart. If a screen is placed 3m away from the double-slit, what will be the distance from the central bright spot on the screen to the next bright spot?
https://www.khanacademy.org/test-pr...agnetic /v/youngs-double-slit-problem-solving

Homework Equations

per KhanAcademy: d*sinθ = m*λ

per what I think: Y = R*m*λ / d

d = distance between the 2 slits
m = whether it's the 1st, 2nd, 3rd bright band
Y = distance from central bright
R = distance from double-slit to screen

The Attempt at a Solution

per KhanAcademy and using d*sinθ = m*λ

d*sinθ = m*λ
1300nm*sinθ = 1*700nm
sinθ = 700nm / 1300nm
θ = 32.6°

then use this to find Y
tanθ = Y / X
Y = tanθ*X
Y= tan(32.6°)*3m
Y= 0.64*3
Y= 1.92mper what I think and using Y = R*m*λ / d

Y = R*m*λ / d
Y = 3m*1*700nm / 1300nm
Y = 1.62m

(nanometers were converted to meters. I just did it this way to save space when typing it here)

My Question: Which equation should I use? Why am I getting different answers?

 

[andrevdh]

The second formula is the small angle approximation:
then sin(θ) ≅ θ in radians and θ ≅ Y/R